# Introduction to Analysis I

MATH 471

#### Instructor:

Lyudmyla Barannyk
317 Brink Hall
tel:  (208) 885-6719
fax: (208) 885-5843
barannyk@uidaho.edu
office hours:
M 2:30-4:00 pm
Th 2:00-3:30 pm
or by appointment

Class discussion mailing list: math471-f08@uidaho.edu

 Handouts

## Course Description

This course is the first half of a year long course in the theory of functions on the real line. Most of the first semester will be spent on a careful examination of sequences, limits of functions, continuity and their applications to differentiation and integration. This analysis will produce strong results about real functions that surpass the calculus, as well as a rigourous recovery of those theorems. A central methodological theme will be the development of mathematical intuition and proof-writing, by exercising these abilities in unfamiliar contexts.

## Textbook

A Friendly Introduction to Analysis Single and Multivariable   by Witold A.J. Kosmala, 2nd Edition, Prentice Hall.

## Homework

Homework will be assigned on Friday and due on Friday in two weeks after it has been assigned. Late homework will in general not accepted. Homework will consist of two parts: assigned problems and suggested problems. You do not have to turn in the suggested problems, but will be responsible for these problems on the exam. It is important to do all homework  in order to gain a better understanding of the course material.

Homework # 1 (assigned 8/29) -  due on Friday, September 12
Assigned problems:
section 2.1: # 7, 8, 19
section 2.2: # 16, 20
Suggested problems:
section 2.1:  # 1- 4, 15
section 2.2:  # 1, 5, 11, 12

Homework # 2 (assigned 9/12) - due on Friday, September  26
Assigned problems:
section 2.3: # 8, 12
section 2.4: # 11(a,b,j)
section 2.5: # 16, 17 (hints: consider a_{n+2}-a_{n+1} and use an idea of telescoping series
or use an approach from Remarks 1.3.11 and 1.3.12 on pg. 27, Section 1.3)
Suggested problems:
section 2.3: # 5, 6, 7, 17, 19
section 2.4: # 1, 3, 4, 6
section 2.5: # 1, 3, 8

Exam # 1: Friday, September 26 - covers sections 2.1-2.5

Homework # 3 (assigned 10/3) - due on Friday, October  17 - Solutions to HW # 3
section 2.6: # 1, 2
section 3.1: # 10, 12
section 3.2: # 14
Suggested problems:
section 2.5: # 12 (a)
section 2.6: # 7,9
section 3.1: # 1, 5
section 3.2: # 1, 2, 3, 5, 8

Homework # 4 (assigned 10/20) - due on Monday, November 3 - Solutions to HW # 4
section 3.3: # 11
section 4.1: # 5
section 4.3: # 16
Suggested problems:
section 3.3: # 4, 5
section 4.1: # 2, 3, 4
section 4.3: # 1, 3, 5, 15

Exam # 2: Wednesday, November 5 - covers sections 2.6, 3.1-3.3, 4.1 and 4.3

Homework # 5 (assigned 11/3) - due on Friday, December 5
section 4.4: # 11
section 5.1: # 13
section 5.2: # 14, 15
section 5.3: # 6,  9, 10
section 5.4: # 6, 10
Suggested problems:
section 4.4: # 1, 2, 5
section 5.1: # 2, 3(h, i, j),  9
section 5.2: # 1(a, b, l, m), 6, 7, 10, 11
section 5.3: # 1, 4
section 5.4: # 2, 4

Exam # 3: Friday, December 5 - covers sections 4.4, 5.1-5.4   - midterm exam 3

## Exams

There will be three in class midterm exams and take home final exam. Before each exam, we will dedicate one entire class period for review and preparation for the exam.

Midterm Exam 1: Friday, September 26

Exam # 1 covers sections 2.1-2.5. Review also sections 1.2, 1.3, 1.7 and 1.8.

Midterm Exam 2: Wednesday, November 5
Midterm 2 Review Session: Tuesday, November 4, 6 - 7 pm, TLC 041

Midterm Exam 3: Friday, December 5
Midterm 3 Review Session: Wednesday, December 3, 6-7 pm, TLC 041

Final Exam assignment will be distributed on Friday, December 12 and due on Tuesday, December  16 by 2:30 pm.

Final exam - due on Tuesday, December 16 by 2:30 pm